Simplify the following expression: $ q = \dfrac{-9}{k + 1} - 9 $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{k + 1}{k + 1}$ $ \dfrac{9}{1} \times \dfrac{k + 1}{k + 1} = \dfrac{9k + 9}{k + 1} $ Therefore $ q = \dfrac{-9}{k + 1} - \dfrac{9k + 9}{k + 1} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-9 - (9k + 9) }{k + 1} $ Distribute the negative sign: $q = \dfrac{-9 - 9k - 9}{k + 1}$ $q = \dfrac{-9k - 18}{k + 1}$